A Model-Theoretic Characterization of Countable Direct Sums of Finite Cyclic Groups#
Abderezak Ould Houcine · Communications in Algebra · 2005
We prove that an abelian group G is a countable direct sum of finite cyclic groups if and only if there exists a consistent existential theory Γ of abelian groups such that G is embeddable in every model of Γ.